Quantile regression for censored data in haematopoietic cell transplant research

Abstract

One of the most important endpoints in haematopoietic cell transplant research is survival. A common objective is to interrogate which, if any, co-variates correlate with these endpoints. The most common statistical approach uses the Cox proportional hazards model. However, there are several problems and limitations of using this model including assumptions of proportional hazards and homogenous effects. In contrast, results of transplant studies often show non-proportional hazards because of early transplant-related mortality such that there is a survival disadvantage to transplants early on followed by a benefit. Even when a transplant proves better than a comparator not all transplant recipients benefit equally and some may be disadvantaged. Also, the favourable or unfavourable impact of a co-variate may vary in different time intervals. The accelerated failure time model which directly evaluates the association between survival and co-variates has similar limitations. Also, these models confer only a static view of the treatment effect. Several articles in our statistics series such as that by Zhen-Huan Hu and us (Bone Marrow Transplant. 2021 Aug 19. doi: 10.1038/s41409-021-01435-2), by Zhen-Huan Hu, Hai-Lin Wang and us and forthcoming articles by Megan Othus and by Liesbeth C. de Wreede, Johannes Schetelig and Hein Putter discuss issues in proper analyses of survival data from transplant studies including observational databases and randomized controlled trials. Are there better alternatives? A new popular model is quantile regression. In this typescript Bo Wei concisely introduce the quantile regression model for right censored data. He uses data from a Center for International Blood and Marrow Transplant Research (CIBMTR) registry study to show how to use the quantile regression and interpret the results. He also discusses use of quantile regression in complex survival analyses such as competing risk data or non-compliant data. Quantile regression is a natural, powerful approach for analyzing censored data with heterogenous co-variate effects. It has advantages compared with other survival models in depicting the dynamic association between survival outcome and co-variates. It can be applied to other transplant outcomes such as cumulative incidence of relapse, event-free and relapse-free survivals. There is an equation, but only one. Remember: The only thing to fear is fear itself (FDR). Please stick with it and you will be rewarded.Robert Peter Gale MD, PhD, DSc(hc), FACP, FRCP, FRCPI(hon), LHD, DPS, Mei-Jie Zhang PhD.